To verify if $y=\frac{1}{3}$ is a valid solution to the linear equation $9y+2=6y+3$, apply the three-step determination strategy:

Step 1. Substitute the value for the variable: $9\left(\frac{1}{3}\right) + 2 = 6\left(\frac{1}{3}\right) + 3$ Step 2. Simplify expressions on both sides. Multiply first: $3 + 2 = 2 + 3$. Then add: $5 = 5$ Step 3. Determine if the result is true: Since $5 = 5$ is a true mathematical statement, the value $y=\frac{1}{3}$ is confirmed as a solution to the equation.